Digital Image Processing: A Remote Sensing PerspectivePerspectiveFW 5560Lecture 8GtiCtitbitGeometric Corrections-two basic typesImage-to-image registration- useful for registering two or more images together when not necessary to have interpreted output in a formal map projection. Works with the internal file coordinate system.system.Image-to-map rectification- required when preparing images and interpreted output for analysis using a recognized map projectioninterpreted output for analysis using a recognized map projection with a known ellipse and datum.Image-to-Map Geometric Rectification- is most widely adopted geometric correction methodologygeometric correction methodologySpatial Interpolation uses a coordinate transformation, pp ,manipulates the “framework” of the image.Intensity Interpolation populates the transformedIntensity Interpolation populates the transformed framework with digital values.Spatial Interpolation1storder, six-parameter, affine transformation- rectify the imagery to a geographic frame of reference:ybxbbyyaxaax210''++++=ybxbby210'++=where:where:x and y are positions in the output-rectified image or mapx’ and y’ represent corresponding positions in the originalinput image.Order approximationsOriginalf1stordersurface2ndorder3rdorderAffine TransformationAffine Transformationyaxaax210'++=ybxbbyyaxaax210210' ++=++This first order transformation can model six kinds of distortion in the remote sensor data, including:• translation in x and y,•scalechanges inxandyscalechanges in xand y,• skew, and • rotation.Use of GCPs (Ground Control Points) and their interaction with RMSRMSAll of the original GCPs selected are usually not used to tthfi litffiitdttdcompute the final six-parameter coefficients and constants used to rectify the input image.Iterative process- First, all of the original GCPs (e.g., 20 GCPs) are used to compute an initial set of six coefficients and constants.constants.Root mean squared error (RMS) is calculated with these initial 20 GCPs If RMS is too large GCPs e al ated20 GCPs. If RMS is too large, GCPs evaluatedIndividual GCPs that contributed the greatest amount of error areIndividual GCPs that contributed the greatest amount of error are deleted. S d it ti i d RMS l l t dSecond iteration is run and new RMS calculated.Process continues until the RMSE reaches a user-specified threshold. Goal is to remove the GCPs that introduce the most error into theGoal is to remove the GCPs that introduce the most error into the multiple-regression coefficient computation.Wh th t bl th h ld i h d th fi l ffi i tWhen the acceptable threshold is reached, the final coefficients and constants are used to rectify the input image to an output image in the specified coordinate system.Measure the accuracy of a geometric rectification algorithm (actually, its coefficients) is to compute the Root Mean Squared Error (RMSerror) for each ground control point using the equation:()( )22origorigerroryyxxRMS −′+−′=where:dii ldlxorigand yorigare originalrow and column coordinates of the GCP in the image and x’andy’are thecomputed or estimatedand yare the computed or estimatedcoordinatesPointPointOrder ofOrder ofEasting onEasting onNorthingNorthingX’ pixelX’ pixelY’ PixelY’ PixelTotal RMSTotal RMSPoint Point NumberNumberOrder of Order of Points Points DeletedDeletedEasting on Easting on MapMapX1X1Northing Northing on Mapon MapY1Y1X’ pixelX’ pixelY’ PixelY’ PixelTotal RMS Total RMS error after error after this point this point deleteddeleted1112125971205971203 627 053 627 051501501851850 5010 5011112125971205971203,627,053,627,05001501501851850.5010.50122 99 597,680597,680 3,627,803,627,80 166166 165165 0.6630.66300…..…..2020 11 601,700601,700 3,632,583,632,5800283283 1212 8.5428.542If we delete CP #20, the Total RMS error with Total RMS error with allall 20 GCPs used:20 GCPs used:11.01611.016RMSE will be 8.452Intensity InterpolationGoal is to fill registered fkhiiframework that is in a standard map projection with the appropriate values from the original data.ybxbbyyaxaax210210''++=++=ybxbby210++yxx)0054810(03418702366382'−++−=yxyyxx)0349150.0()005576.0(130162')005481.0(034187.02366.382−+−+=++=There are several intensity interpolation (resampling)algorithms, including:Nearest NeighborBili I t l tiBilinear InterpolationCubic ConvolutionNearest-Neighbor ResamplingDN closest to predicted x’, y’ coordinate is assigned to the output x, y coordinate.Bilinear Interpolation Assigns output DNs by caculating weighted distance of the 4our surroung pixels of the coordinate in question. Closer a pixel is to the desiredx’,y’location, the more weight it will have in the finalthe desired x,y location, the more weight it will have in the final computation of the average. 4Z∑==12kkkDZBVwhere Zkare the surrounding four data point values, and D2kare the distances squared from the point in question (x’, y’) to the these data points. ∑=4121kkwtDBVpq (y)p=1kkD∑42kZ∑∑==4121kkwtDBV∑=12kkDCubic Convolution Assigns values to output pixels in much the same manner as bilinear interpolation except that the weighted values of16bilinear interpolation, except that the weighted values of 16pixels surrounding the location of the desired x’, y’ pixel are used to determine the value of the output pixel.∑162kZwhereZkare the surrounding four data point values, ∑∑==16121kkwtDBVkgpand D2kare the distances squared from the point in question (x’, y’) to the these data points.